The answer is that it depends on whether you were already handling a keyboard interrupt.
Most interrupt service routines (ISR) have code at the termination of them which informs the hardware that it has been "serviced." In the case of the keyboard controller, commands are written to it acknowledging the received bytes. It is at the time of acknowledgement that the keyboard controller hardware stops using electricity to signal an interrupt condition.
If you are handling a non-keyboard interrupt, let's say the fire alarm interrupt, then the keyboard hardware which electrically asserts the interrupt will trigger as the key is pressed. The electrical signal is ignored until the CPU has interrupts enabled again. At the end of servicing the fire alarm interrupt, the fire alarm ISR acknowledges whatever data and re-enables interrupts on the CPU. Immediately, the CPU enters an interrupt because the keyboard controller is still electrically signalling an interrupt condition.
If you are handling a keyboard interrupt, and the user quickly types a second keystroke during the execution of your keyboard ISR, then there is a chance of missing the data from the second keystroke, or of receiving it later if at all. In particular, if the ISR resets the keyboard controller through an acknowledge, but the ISR has not actually received all the available bytes out of the keyboard controller, then that is a problem.
Often, an ISR will first handle the interrupt which triggered its activation, then after acknowledging the interrupt, poll the device to see if it has received more data since the first interrupt. If so, generate a software interrupt to re-enter the ISR and service the device.